In a class of 150 ​students, 94 are taking math​ (M), 76 are taking science​ (S), and 52 are taking both math and science. One student is picked at random. Find the probability.
​P(taking math or science or​ both)
M
S
42
52
24
32
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Part 1
​P(taking math or science or ​both)equals
  
enter your response here
​(Round to three decimal places as​ needed.)

To calculate the probability \( P(\text{taking math or science or both}) \), we use the principle of inclusion-exclusion. The formula for the union of two sets \( M \) and \( S \) is:

\[
P(M \cup S) = P(M) + P(S) - P(M \cap S)
\]

### Given Information:
- Total number of students = \( 150 \)
- Number of students taking math (\( |M| \)) = \( 94 \)
- Number of students taking science (\( |S| \)) = \( 76 \)
- Number of students taking both math and science (\( |M \cap S| \)) = \( 52 \)

### Step 1: Calculate the probability for each set
- Probability of taking math:  
  \[
  P(M) = \frac{|M|}{\text{Total students}} = \frac{94}{150}
  \]

- Probability of taking science:  
  \[
  P(S) = \frac{|S|}{\text{Total students}} = \frac{76}{150}
  \]

- Probability of taking both math and science:  
  \[
  P(M \cap S) = \frac{|M \cap S|}{\text{Total students}} = \frac{52}{150}
  \]

### Step 2: Apply the formula
\[
P(M \cup S) = P(M) + P(S) - P(M \cap S)
\]
Substitute the values:
\[
P(M \cup S) = \frac{94}{150} + \frac{76}{150} - \frac{52}{150}
\]

Simplify:
\[
P(M \cup S) = \frac{94 + 76 - 52}{150} = \frac{118}{150}
\]

### Step 3: Round to three decimal places
\[
P(M \cup S) = 0.787
\]

### Final Answer:
The probability that a student is taking math, science, or both is:
\[
\boxed{0.787}
\]

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Do you want a breakdown of additional details or related concepts?  

### Related Questions:
1. What is the probability that a student is only taking math but not science?  
2. What is the probability that a student is only taking science but not math?  
3. How many students are not taking either math or science?  
4. How would the result change if 10 more students were taking both subjects?  
5. What is the complement of \( P(M \cup S) \), and how is it calculated?  

### Tip:
When working with probabilities involving multiple sets, always remember to subtract the overlap (intersection) to avoid double counting!

In a class of 150 students, 94 are taking math (M), 76 are taking science (S), and 52 are taking both math and science. One student is picked at random. Find the probability P(taking math or science or both).

Learn how to calculate the probability that a student is taking math, science, or both in a class of 150 students, where 94 are taking math, 76 are taking science, and 52 are taking both. Step-by-step solution using the inclusion-exclusion principle.

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